In imaging lenses, various aberrations must be corrected through cascading many lenses made of different materials and curvatures. This causes imaging lenses bulky, heavy and complex. Here, we demonstrate a metasurface aberration corrector (meta-corrector), comprising only a layer of 600-nm-thick TiO2 nanostructures, capable of rendering a single refractive plano-convex lens achromatic and free of spherical aberration in a compact manner across the visible spectrum. Our approach is based on, for any incident polarization, compensating the glass dispersion and correcting the curvature error of the spherical lens by tailoring phase, group delay and group delay dispersion of each meta-corrector’s nanostructure. The resultant metasurface-refractive lens has a diameter and f-number of 1.5 mm and 6.6, respectively, and is diffraction-limited from wavelength of 460 to 700 nm. The generality of our design method can be applied to extremely complicated refractive optics. As an example, we show a meta-corrector that greatly increases the bandwidth of a state-of-the-art immersion objective from the violet to near-infrared wavelengths. The objective, consisting of 14 lenses and 7 different materials, has a numerical aperture of 1.45 and is commercially available from Zeiss. Metasurface-refractive optics combines the advantages of both technologies in terms of size scalability and complexity for many applications such as imaging, augmented reality and lithography.